| Summary: | Most real time series exhibit certain characteristics that make the choice of model and its specification difficult. The objective of this study is to address the problem of parameter estimation and the accuracy of forecasts <i>k</i>-steps ahead in non-stationary time series with outliers in the context of state-space models. In this paper, three methods for detecting and treating outliers are proposed. We also present a comparative study of the proposed methods using data simulated from a local level model with sample sizes of 50 and 500 and with various combinations of parameters, with a 5% contamination error rate of the observation equation. The results were evaluated in terms of the accuracy of model parameters and the forecasts <i>k</i>-steps ahead, as well as the detection rate of true outliers. These methodologies are applied to three real examples. This study shows that the local level model is sufficiently robust even for non-stationary contaminated series, in the sense that they are able to handle non-stationary time series and outliers in a satisfactory way.
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